Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle (7,4,-4), (1,-1,1), and (-8,-1,3) the midpoints of the opposite sides.

Q: Find the sum of the vectors (–1,4) and (6, –2) and illustrate geometrically.

A: A vector V→=a,b can be represented on the cartesian plane, From the vector law of addition,…

Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

A:

Q: Find area of triangle whose vectors Р (3,3, 1), Р2-1,0,2), Р3(2,3,3)

A:

Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: Express the vector (-1, 0) as a linear combination of the vectors (-1, - 1) and (-1, 1). (-1,0) =…

A:

Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: The two vectors a = (-1,2,-2) and b = (2, -4,-5), are not parallel but are orthogonal. Select one:…

A: Using algebraic operation

Q: Dilate the vector (-3,5) by a factor of 3. ([ ? ],[])

A: Given vector: V=-3, 5 ……1   Also, Scalar factor is 3.

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

A:

Q: Find the sum of the given vectors. a - (3, 0, 2), b- (0, 6, 0) Illustrate geometrically.

A: Given, Two vectors  a = ⟨3, 0, 2⟩   b = ⟨0, 6, 0⟩  We have to find the sum of vectors and illustrate…

Q: photo attached

A: Given that a vector V goes from the origin to a point (5, -5).

Q: Graph the two vectors x= (5, 1,3) and y=(-1,3,1

A: Topic:- 3D

Q: What is the terminal point of the vector a = (2, 2) based at P = (2,4)?

A:

Q: 1. Find the resultant of the vectors A and B. A = 8a, + 7a, + 2a, В - - За, — 8а, - ба, Draw the…

A: Given that: A→=8ax+7ay+2azB→=-3ax-8ay-6az

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: Find the vector that has the same direction as (6, 2, -3) but has length 2.

A:

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: Find four different nonzero vectors that are orthogonal to v = (-1,5,2)

A: This is a simple problem based on orthogonal vector which could be solved by using basic knowledge…

Q: Determine which vectors that are orthogonal to (-3,- 6)? (-4,2) and (- 1,3) (-10, 5) and (-3, 6) a.…

A: Since your question has multile question we will solve the first question for you.   Find the…

Q: Write the vector (7,8, –8) as a linear combination (if possible) as of the vectors (-1,1,2), (2,3,…

A: See answer below

Q: Select all vectors parallel to the vector (1,-3, 5). O (2, -6, 10) 0(-1,3,6) - 15

A: here to we need to find the parallel vectorsto the given vector from the given options. the solution…

Q: 2) Subtract the (2) vectors; (4, 6) & (-8, -10)

A: The given vectors are 4, 6 and -8, -10 We need to subtract the given vectors.

Q: The normal vector of 2x + By - 16.7z = -8 is: ○ [2, 뮤, -16.7, 8) ① [호, 꽃, 16.7, -8] ① [올, 꽃, -16.7]…

A: We have given equation of a plane  92x+133y-16.7z=-8 Comparing this with the equation  lx+my+nz=d We…

Q: Find the vector that has the same direction as (3, 2, -6) but has length 5.

A: Just follow the flow and you are done.

Q: Find a vector that has the same direction as (-4, 6, 4) but has length 6.

A: we have to find a vector that the same direction as <-4, 6, 4> but has length 6

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: Determine if the vectors (2, –2, 1) and (0,1, 2) are orthogonal.

A:

Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

A:

Q: Determine which vectors that are orthogonal to (– 3, -6)? (-4,2) and (-1,3) (-10, 5) and (-3, 6) a.…

A: To determine the vectors which are orthogonal to -3,-6. (a) Given vectors are -4,2 and -1,3. We know…

Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

A:

Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

A:

Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0).

A: Unit Vectors orthogonal to vectors  <2,3,1> and <-1,1,0>…

Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

Q: Write the vector (7, 8, -8) as a linear combination (if possible) as of the vectors (-1, 1, 2), (2,…

A: Let the linear combination be, x-112+y23-2=78-8 It is required to determine the value of 'x' and 'y'…

Q: Find the sum of the vectors (3,0,1) and (0,8, 0) and illustrate geometrically.

A: Solved below

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

A:

Q: find two unit vectors orthogonal to (5,-5,3) and (-3,5,2)

A:

Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

A:

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

A:

Q: What position vector is equal to the vector from (- 2,9,3) to (-5, - 6,8)? The position vector is…

A: We have to find

Q: Is it possible to write the vector (-5,11,-7) as a linear combination of the vectors…

A: See the attachment

Q: Find two vectors V1 and V2 whose sum is ⟨2,−5,3⟩, where V1 is parallel to ⟨4,4,0⟩ while V2 is…

A: Parallel vector will be multiple of each other  Perpendicular vector has dot products zero

Q: Write the vector (7, 4,-12) vectors (-2, 1, 2), (1, 1, –2) as a linear combination (if possible) as…

A:

Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

A:

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: find two unit vectors orthogonal to (-1,-1,5) and (-5,-,3,3)

A:

Q: )Find the vector in R2 from point A = (8,9) to B = (-3,5). AB = help (vectors)

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.